People write songs in several ways. Some are just inspired and write what comes into their heads, and soon it's on paper and out in front of a crowd. Others pore over their note-paper, their computers, their guitars and keyboards, picking out the right chords and the right words. But there are a few simple methods for the beginner.

Method 1: Words first
Method 2: Tune first
Method 3: Together

Read lots of poetry. Read the kind of poetry you like and you'll begin to write like that too.
Learn how to write poetry. You can begin here.
Learn how to sing. You don't have to be Madonna, but you should be able to carry a tune with the right pitches and a decent sense of rhythm. Learn how to sing here.
If you can, learn how to read music of some sort, whether guitar notation or standard western classical, it helps to know there are 7 basic notes A-G, what a quarter or half and whole note are, what the treble and bass clef are.
Sing in the shower. Make up your own tunes to songs you know, or hum random assemblages of notes. No one's in there to know or care if you're wrong.
Keep writing and trying out different tunes or words for a song. Eventually there'll be one that fits.

Method 1: Words first

1. Write a poem.
2. Ballads are usual for songs (4 lines of 4 or 8 beats each per stanza), but you can use anything, with or without a defined rhythm.
3. Set a beat to it, if you like. Keep it a steady beat that reflects the character of the song in some way.
5. Now add the tune. Make it up as you go along, or make the chorus (the main part of the song) first, then go back and redo the stanzas. You can even take a song you know, change several of the notes, and use or change the rhythm to make a new song. Make sure it's not obviously derived though.
6. Add instruments. If you can play an instrument, great. Play the accompaniment as just chords or separate sections or actual melody or harmony. Percussion can be done by a drummer or beats on tin cans or a synthesizer/keyboard.
7. Record your song by writing it down on paper if you can. Even if you don't, sing it or perform it and record onto tape, CD, etc.

Method 2: Tune first

1. Many people prefer to write the words after getting a tune. This may or may not be easier for you, but also keep in mind that not all tunes have to have words.
2. Maybe you've hummed a tune or can play one. Put together musical phrases on an instrument or just with your voice. It will have a rhythm of its own.
3. Once you have a tune, think of the mood it creates. Is it sad, happy, nostalgic, fierce, playful? You'll want words that fit the music. Or maybe you want them opposite!
4. Write words for the rhythm of the piece. Laaa, la, la, la, thus needs 4 syllables to be best. You can extend words if you like, but it should sound write. Obviously, it's harder to fit You're pretty into those four than it is You're beautiful.
5. Often it's easiest to put together the words of the chorus or just a stanza and the chorus, and once that feeling is in place, the next stanza comes together based on the original mood and theme of the lyrics.

Method 3: Together

1. Sometimes, words and tune come along. As you hum, you already have words that fit nicely in your song.
2. This is a great method to use in the shower. Just sing and let whatever words fit in the song come in. When you have a stanza and a chorus, sing them a few times so you don't forget, then record them or write them down.
3. What you come up with may be nonsensical words, but a few key phrases may come up, or just your sudden feelings. Go with that, edit as necessary.
4. Finally, put the finishing touches on your piece by recording with full instruments, percussion, voice, etc. You've written a wonderful song!